Home › Exam notes › SSC CGL › Time & Work

Time & Work

Quantitative Aptitude / DI · Arithmetic Applications

Useful for: SSC CGL, Railway RRB, IBPS Banking, CTET, OTET, OSSTET, UGC NET, OSSC RHT — Regular High School Teacher

and 22 more exams

UPSC NDA/NA, CSIR NET, CTSA / STSS, Central Univ./IIT/NIT Faculty, Junior Teacher, OAVS, OPSC Assistant Professor, OPSC PGT, OSEPA Primary Teacher / JT Category-I, OSEPA Upper Primary — Science, OSSC Mathematics, OSSC Teacher Readiness, OSSSC Govt Physical Education Teacher (PET), OSSSC Govt TGT Arts, OSSSC Govt TGT Science — CBZ, OSSSC Govt TGT Science — PCM, Sainik Schools, Special OTET, SSB Lecturer / PGT, SSB Lecturer (Degree Colleges), SSB School Teachers, SSB TGT PCM

हिंदी में पढ़ें

Overview

Work = efficiency × time; taking total work as the LCM of the given days turns fractions into whole units.

Key points

If A finishes in a days, A’s one-day work = 1/a.
Together: 1/a + 1/b; time = ab/(a + b).
Total-work method: take LCM of days as work units, find units per day.
Pipes: a filling pipe adds, an outlet subtracts; net rate = fill − empty.
Efficiency is inversely proportional to time.

Explanation

If A is k times as efficient as B, A takes 1/k of B’s time.
Left-the-work problems: compute work done in the shared period, then the remainder by the one who stays.
Wages are shared in the ratio of work done, not days worked.
A leak converting fill time t1 to t2: leak alone empties in t1·t2/(t2 − t1).

Step by step

Set total work = LCM.
Find each rate in units per day.
Combine and divide.

Examples

A takes 10 days, B 15 days → together 1/10 + 1/15 = 1/6 → 6 days.
Pipe A fills in 12 h, outlet B empties in 18 h → net 1/12 − 1/18 = 1/36 → 36 h.
A is twice as efficient as B; together they take 12 days → work = 3 × 12 = 36 units → B (1 unit/day) alone 36 days.

Traps and advanced points

Trap: Adding days instead of rates.
Trap: Treating an outlet as a filling pipe.
Trap: Sharing wages by days rather than work done.

Quick revision

Work = rate × time.
LCM method avoids fractions.
Net pipe rate = fill − empty.

Practice MCQs

A can finish a job in 64 days and B in 126 days. How many days will they take together?
1. 48.81
2. 42.44
3. 36.08
4. 55.17
Read chapter notes · Similar questions
Show answer
Answer: (b) 42.44. Add work rates: 1/A + 1/B.
A can finish a job in 75 days and B in 148 days. How many days will they take together?
1. 42.31
2. 64.71
3. 49.78
4. 57.24
Read chapter notes · Similar questions
Show answer
Answer: (c) 49.78. Add work rates: 1/A + 1/B.
A can finish a job in 86 days and B in 170 days. How many days will they take together?
1. 48.54
2. 57.11
3. 65.68
4. 74.24
Read chapter notes · Similar questions
Show answer
Answer: (b) 57.11. Add work rates: 1/A + 1/B.
A can finish a job in 97 days and B in 192 days. How many days will they take together?
1. 64.44
2. 54.78
3. 83.78
4. 74.11
Read chapter notes · Similar questions
Show answer
Answer: (a) 64.44. Add work rates: 1/A + 1/B.
A can finish a job in 108 days and B in 214 days. How many days will they take together?
1. 61.01
2. 82.54
3. 71.78
4. 93.31
Read chapter notes · Similar questions
Show answer
Answer: (c) 71.78. Add work rates: 1/A + 1/B.
A can finish a job in 46 days and B in 90 days. How many days will they take together?
1. 35.01
2. 30.44
3. 25.88
4. 39.57
Read chapter notes · Similar questions
Show answer
Answer: (b) 30.44. Add work rates: 1/A + 1/B.
A can finish a job in 47 days and B in 92 days. How many days will they take together?
1. 26.44
2. 31.11
3. 35.77
4. 40.44
Read chapter notes · Similar questions
Show answer
Answer: (b) 31.11. Add work rates: 1/A + 1/B.
A can finish a job in 53 days and B in 104 days. How many days will they take together?
1. 45.64
2. 40.37
3. 29.84
4. 35.11
Read chapter notes · Similar questions
Show answer
Answer: (d) 35.11. Add work rates: 1/A + 1/B.
A can finish a job in 59 days and B in 116 days. How many days will they take together?
1. 44.97
2. 39.11
3. 33.24
4. 50.84
Read chapter notes · Similar questions
Show answer
Answer: (b) 39.11. Add work rates: 1/A + 1/B.
A can finish a job in 96 days and B in 190 days. How many days will they take together?
1. 63.78
2. 82.91
3. 73.34
4. 54.21
Read chapter notes · Similar questions
Show answer
Answer: (a) 63.78. Add work rates: 1/A + 1/B.
A can finish a job in 20 days and B in 38 days. How many days will they take together?
1. 15.07
2. 11.14
3. 13.1
4. 17.03
Read chapter notes · Similar questions
Show answer
Answer: (c) 13.1. Add work rates: 1/A + 1/B.
A can finish a job in 14 days and B in 26 days. How many days will they take together?
1. 10.46
2. 9.1
3. 11.83
4. 7.73
Read chapter notes · Similar questions
Show answer
Answer: (b) 9.1. Add work rates: 1/A + 1/B.
A can finish a job in 103 days and B in 204 days. How many days will they take together?
1. 68.44
2. 78.71
3. 88.98
4. 58.18
Read chapter notes · Similar questions
Show answer
Answer: (a) 68.44. Add work rates: 1/A + 1/B.
A can finish a job in 68 days and B in 134 days. How many days will they take together?
1. 51.88
2. 58.64
3. 45.11
4. 38.34
Read chapter notes · Similar questions
Show answer
Answer: (c) 45.11. Add work rates: 1/A + 1/B.
A can finish a job in 15 days and B in 28 days. How many days will they take together?
1. 11.23
2. 8.3
3. 9.77
4. 12.7
Read chapter notes · Similar questions
Show answer
Answer: (c) 9.77. Add work rates: 1/A + 1/B.